The foundations of statistical physics: entropy, irreversibility, and inference

TL;DR

This paper reviews the foundational role of entropy in statistical physics, emphasizing the maximum entropy principle for equilibrium states and introducing maximum caliber as a variational principle for non-equilibrium systems, linking it to various approaches.

Contribution

It clarifies the foundational principles of entropy in non-equilibrium physics, highlighting maximum caliber as a key variational principle and connecting it with existing theories.

Findings

Maximum Caliber maximizes path entropy for non-equilibrium systems.

Entropy characterizes irreversibility in statistical physics.

MaxCal relates to Stochastic Thermodynamics, Large Deviations, and other approaches.

Abstract

Statistical physics aims to describe properties of macroscale systems in terms of distributions of their microscale agents. Its central tool is the maximization of entropy, a variational principle. We review the history of this principle, first considered as a law of nature, more recently as a procedure for inference in model-making. And while equilibria (EQ) have long been grounded in the principle of Maximum Entropy (MaxEnt), until recently no equally foundational generative principle has been known for non-equilibria (NEQ). We review evidence that the variational principle for NEQ is Maximum Caliber. It entails maximizing \textit{path entropies}, not \textit{state entropies}. We also describe the role of entropy in characterizing irreversibility, and describe the relationship between MaxCal and other prominent approaches to NEQ physics, including Stochastic Thermodynamics (ST), Large Deviations Theory (LDT), Macroscopic Fluctuation Theory (MFT), and non-extensive entropies.